Controlling Transport of Bose-Einstein Condensates with a Tunable Synthetic Magnetic Flux

Manipulating quantum systems with external fields is fundamentally important for quantum science and technology. For example, giant magnetoresistance, where the electronic transport is tunable by an external magnetic field, has rich applications such as memory devices. Highly controllable atomic systems offer opportunities to observe phenomena inaccessible in conventional platforms, such as exploring physics inherent in spaces beyond planar geometries . Here, we realize a Bose-Einstein condensate (BEC) on a synthetic topological Hall cylinder subject to net radial and axial synthetic magnetic fluxes. We observe the emergence of symmetry-protected topological band crossings absent in planar spaces. Breaking the symmetry induces a topological transition manifested as gap opening at band crossings and further allows for controlling BEC's transport with a tunable synthetic axial magnetic flux. We calibrate this axial flux by performing quench experiments and employ it to control spin compositions of the BEC during transport, reminiscent of a "magnetotransport" behavior. Our work provides insights into utilizing unconventional spaces to realize novel atomtronic devices.